Question

Which has a higher percentage of nitrogen: carbamazepine, an anticonvulsant, \(\left(\mathrm{C}_{15} \mathrm{H}_{12} \mathrm{~N}_{2} \mathrm{O}\right)\) or carbetapentane, a cough suppressant, \(\left(\mathrm{C}_{20} \mathrm{H}_{31} \mathrm{NO}_{3}\right)\) ?

Short answer

Carbamazepine has a higher percentage of nitrogen than carbetapentane.

Step-by-step solution

Calculate the molar mass of carbamazepine

Determine the molar mass of carbamazepine by adding the atomic masses of each element in the formula. The formula is (C15H12N2O), so its molar mass is: 15 * C (carbon) + 12 * H (hydrogen) + 2 * N (nitrogen) + 1 * O (oxygen), using the periodic table for the atomic masses.

Calculate the molar mass of nitrogen in carbamazepine

Calculate the molar mass of nitrogen in the carbamazepine molecule by multiplying the atomic mass of nitrogen by the number of nitrogen atoms in the molecule, which is 2.

Calculate the percentage of nitrogen in carbamazepine

Divide the molar mass of nitrogen in carbamazepine by the total molar mass of carbamazepine and multiply by 100 to get the percentage of nitrogen.

Calculate the molar mass of carbetapentane

Determine the molar mass of carbetapentane by adding the atomic masses of each element in the formula. The formula is (C20H31NO3), so its molar mass is: 20 * C + 31 * H + 1 * N + 3 * O.

Calculate the molar mass of nitrogen in carbetapentane

Calculate the molar mass of nitrogen in the carbetapentane molecule, which has one nitrogen atom.

Calculate the percentage of nitrogen in carbetapentane

Divide the molar mass of nitrogen in carbetapentane by the total molar mass of carbetapentane and multiply by 100 to determine the percentage of nitrogen.

Compare the percentages

Compare the percentages of nitrogen in both compounds to determine which one has a higher percentage.

Key concepts

Molar Mass Calculation

To determine which compound has a higher percentage of nitrogen, the first step is understanding molar mass calculation. Molar mass is the sum of the atomic masses of all atoms in a molecule and is expressed in grams per mole (g/mol). Each element has a standard atomic mass, for instance, carbon (C) is approximately 12.01 g/mol, hydrogen (H) is about 1.008 g/mol, and nitrogen (N) is roughly 14.01 g/mol.

By multiplying these atomic masses by the number of each type of atom in the compound's formula, you can calculate the compound's molar mass. For example, carbamazepine has 15 carbon atoms, 12 hydrogen atoms, 2 nitrogen atoms, and one oxygen atom. Thus, its molar mass is calculated by summing up 15 times the atomic mass of carbon, 12 times the atomic mass of hydrogen, 2 times the atomic mass of nitrogen, and once the atomic mass of oxygen.

Stoichiometry

Stoichiometry is a field of chemistry that involves the quantitative relationships of the reactants and products in a chemical reaction. In this context, stoichiometry pertains to understanding the ratio of nitrogen to the other elements in a compound, which helps determine the proportion of nitrogen present in each molecule.

Once the molar mass of a compound is known, stoichiometry allows us to calculate the percentage composition of each element. To find the percentage of nitrogen in a compound, the molar mass of the nitrogen atoms is divided by the total molar mass of the compound and multiplied by 100. This will give us the fraction of the compound's mass that is due to nitrogen, which is vital for comparing different compounds containing this element.

Chemical Composition Analysis

Chemical composition analysis involves breaking down a compound into its constituent elements to understand what it's made of and in what proportions. Knowing the chemical composition is crucial for a range of applications, including medication efficacy, as seen in the exercise with carbamazepine and carbetapentane.

As per the steps provided, after calculating the molar masses of both compounds, the molar mass attributed to nitrogen is isolated. Dividing this mass by the total molar mass of the compound and multiplying by 100 provides the percentage of nitrogen. Such analysis can prove essential in various fields, such as pharmacology, where the percentage of an element like nitrogen can influence the drug's properties and how it interacts with biological systems.